Greatest Common Factor of 106 and 109

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

• Greatest Common Factor of 106 and 109 by prime factorization method
• Greatest Common Factor of 106 and 109 by matching factors method

Prime Factorization of 106

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 2¹×53¹

Prime Factorization of 109

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 109¹

∴ So by taking common prime factors GCF of 106 and 109 is 1

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1,109

Greatest Common Factor

We found the factors and prime factorization of 106 and 109. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 109 is 1.

Also check out the Least Common Multiple of 106 and 109

(i) The GCF of 106 and 109 is associative

GCF of 106 and 109 = GCF of 109 and 106

1. What is the GCF of 106 and 109?

Answer: GCF of 106 and 109 is 1.

2. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

3. What are the Factors of 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

4. How to Find the GCF of 106 and 109?

Answer:

Greatest Common Factor of 106 and 109 = 1

Step 1: Find the prime factorization of 106

106 = 2 x 53

Step 2: Find the prime factorization of 109

109 = 109

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = = 1

Step 4: Therefore, the greatest common factor of 106 and 109 is 1